When Christopher Uriarte, 36, sits down to a dinner at Eleven Madison Park in New York, it isn't only the food he's excited about—it's the show. The restaurant serves several dishes prepared or finished by the chef at tableside. A carbonated egg cream is prepared on a cart. A raw carrot put through a meat grinder clamped to the table is carrot tartare. "The spectacle adds to the experience," says Mr. Uriarte, a financial-services executive who visits the restaurant, with its $225 prix fixe menu, about twice a year.